Vector Lattice Powers:f-Algebras and Functional Calculus

Однородные Ортогонально Аддитивные Полиномы В Векторных Решетках

“…Введем специальный полином, играющий роль степенной функции в наших рассуждениях. При этом ключевым инструментом является конструкция степени векторной решетки, введенная в работе [10].…”

A Radon–Nikodým type theorem for orthosymmetric bilinear operators

“…The class of orthosymmetric bilinear operators in vector lattices was introduced by G. Buskes and A. van Rooij in [6] and received much attention in succeeding years, see [2,3,5,7,9,14,15]. An inseparable companion of the orthosymmetric bilinear operators turns out to be the concept of square of vector lattice, developed by the same authors in another paper [7].…”

“…In Sect. 3 we prove some new facts concerning the structure of the square of a vector lattice and characterize orthoregular bilinear operators that may be presented as differences of symmetric lattice bimorphisms. A Radon-Nikodým type theorem for orthosymmetric order continuous order interval preserving bilinear operators is discussed in Section 4 and Section 5 contains some concluding remarks.…”

Vector lattices and $f$ -algebras: The classical inequalities

“…In particular, [13] presents a relationship between the Cauchy-Schwarz inequality and the theory of multilinear maps on vector lattices, built on the analogy between disjointness in vector lattices and orthogonality in inner product spaces. The ideas in [13] led to the construction of powers of vector lattices (see [9,14]), a theory that was recently extended to the complex vector lattice environment in [11]. This paper follows the complex theme of [11] and in fact contains results that are valid for both real vector lattices and complex vector lattices.…”